S = 2 decay in Warped Extra Dimensions
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1 S = 2 decay in Warped Extra Dimensions Faisal Munir IHEP, Beijing Supervisor: Cai-Dian Lü HFCPV CCNU, Wuhan October 28, 2017 based on: Chin. Phys. C41 (2017) [arxiv: ] F. Munir (IHEP) New Physics 1 / 14
2 Outline Introduction b ss d decay in the RS model with custodial protection b ss d decay in the bulk-higgs RS model Summary F. Munir (IHEP) New Physics 2 / 14
3 Introduction to RS model 5D spacetime with warped metric [Randall, Sundrum, Phys. Rev. Lett. 83, 3370 (1999)] ds 2 = e 2kr φ η µν dx µ dx ν r 2 dφ 2, φ [ π, π]. The fundamental scale is M P l, and the effective 4D electroweak scale is suppressed by a magic exponential M EW e krπ M P l TeV. natural explanation of gauge hierarchy problem. hierarchical structure of zero mode fermion profiles Light fermions live close to UV brane. Third generation localized closest to the IR brane. Kaluza-Klein (KK) excitations live close to the IR brane. Warped extra dimensions with bulk fields have explanation for fermion masses and CKM hierarchies. Tree level FCNCs (b ss d). F. Munir (IHEP) New Physics 3 / 14
4 b ss d Channel Local S = 2 SM effective Hamiltonian for b ss d transition ( ( ) ( )) H S=2 eff = G2 F m 2 W V 16π 2 td VtsV tb VtsS m 2 t 0 + V m 2 cd VcsV tb VtsS m 2 c 0, m2 t W m 2 W m 2 W [( sd) V A( ) V A] B(B + K + K + π ) < b u,c,t W W+ s [R. Aaij et al. (LHCb), Phys. Lett. B765, 307 (2017)] b ss d decay with very small strength in the SM serves as a sensitive probe for new physics. s ū, c, t d B(b ss d) SM = (2.19 ± 0.38) F. Munir (IHEP) New Physics 4 / 14
5 b ss d decay in the RS c model The RS c model is based on a single warped extra dimension with the bulk gauge group SU(3) c SU(2) L SU(2) R U(1) X P LR b ss d decay receives tree level contributions from the Kaluza-Klein (KK) gluons, the heavy KK photons, new heavy electroweak (EW) gauge bosons Z H and Z, and in principle the Z 0 boson. Custodial protection of the Zb L bl coupling through the discrete P LR symmetry renders tree-level Z 0 contributions negligible. The effective Hamiltonian for the S = 2 b ss d decay with the Wilson coefficients corresponding to µ = O(M g (1)) [H S=2 1 LL eff ] KK = [CV 2(M g (1) ) 2 1 Q V 1 LL + C1 V RR Q V 1 RR + C LR 1 Q LR 1 + C LR 2 Q LR 2 + C RL 1 Q RL 1 + C RL 2 Q RL 2 ]. b s b s G (1) µ Z,Z,ZH,A (1) s d s d F. Munir (IHEP) New Physics 5 / 14
6 b ss d decay in the RS c model Q V LL 1 = ( sγ µp L b)( sγ µ P L d), Q V RR 1 = ( sγ µp R b)( sγ µ P R d), Q LR 1 = ( sγ µp L b)( sγ µ P R d), Q LR 2 = ( sp L b)( sp R d), Q RL 1 = ( sγ µp R b)( sγ µ P L d), Q RL 2 = ( sp R b)( sp L d), [ C V LL 1 (M g (1) )]EW = 2[ L (Z(1) ) sd L (Z(1) ) + L (Z(1) X ) sd L (Z(1) X )], [ C V RR 1 (M g (1) )]EW = 2[ R (Z(1) ) sd R (Z(1) ) + R (Z(1) X ) sd R (Z(1) X )], [ C LR 1 (M g (1) )]EW = 2[ L (Z(1) ) sd R (Z(1) ) + L (Z(1) X ) sd R (Z(1) X )], [ C RL 1 (M g (1) )]EW = 2[ R (Z(1) ) sd L (Z(1) ) + R (Z(1) X ) sd L (Z(1) X )], [C V LL 1 (M g (1) )]G = 2 3 p UV 2 L sd L, [C V RR 1 (M g (1) )]G = 2 3 p UV 2 R sd R, [C LR 1 (M g (1) )]G = 1 3 p UV 2 L sd R, [C LR 2 (M g (1) )]G = 2p UV 2 L sd R, [C RL 1 (M g (1) )]G = 1 3 p UV 2 R sd L, [C RL 2 (M g (1) )]G = 2p UV 2 R sd L, [ C V LL 1 (M g (1) )]QED = 2[ L (A(1) )][ sd L (A(1) )], [ C V RR 1 (M g (1) )]QED = 2[ R (A(1) )][ sd R (A(1) )], [ C LR 1 (M g (1) )]QED = 2[ L (A(1) )][ sd R (A(1) )], [ C RL 1 (M g (1) )]QED = 2[ R (A(1) )][ sd L (A(1) )], F. Munir (IHEP) New Physics 6 / 14
7 b ss d decay in the RS c model C V LL C V RR C LR 1 (M g (1)) = [ ] 1 (M g (1)) = [ ] 1 (M g (1)) = [ ] C1 RL (M g (1)) = [ ] sd L L R L R = 1.25 R = 1.67 sd sd R = 0.25 = 0.25 sd L sd L R L R L, sd R, sd R, sd L, After RG running of the Wilson coefficients to a low energy scale µ b = 4.6 GeV, the decay width in the RS c model Γ = m 5 b LL 3072(2π) 3 [16( CV (M g (1)) 4 1 (µ b ) 2 + C1 V RR (µ b ) 2 ) + 12( C LR 1 (µ b ) 2 + C RL 1 (µ b ) 2 ) + 3( C LR 2 (µ b ) 2 + C RL 2 (µ b ) 2 ) 2Re(C LR 1 (µ b )C LR 2 (µ b ) + C LR 2 (µ b )C LR 1 (µ b ) + C RL 1 (µ b )C RL 2 (µ b ) + C RL 2 (µ b )C RL 1 (µ b ))]. F. Munir (IHEP) New Physics 7 / 14
8 b ss d decay in the bulk-higgs RS model The bulk-higgs RS model is based on the 5D gauge group SU(3) c SU(2) V U(1) Y, where all the fields propagate in the 5D spacetime. b ss d decay in the bulk-higgs RS model results from tree-level exchanges of Kaluza-Klein gluons and photons, the Z 0 boson and the Higgs boson as well as their KK excitations and the extended scalar fields φ Z(n). We consider the summation over the contributions from the entire KK towers, with the lightest KK states having mass M g (1) 2.45 M KK. [H S=2 eff ] KK = 5 [C no n + C n Õ n], n=1 O 1 = ( s Lγ µb L)( s Lγ µ d L), O 2 = ( s Rb L)( s Rd L), O 3 = ( s α Rb β L )( sβ R dα L), O 4 = ( s Rb L)( s Ld R), O 5 = ( s α Rb β L )( sβ L dα R). F. Munir (IHEP) New Physics 8 / 14
9 b ss d decay in the bulk-higgs RS model C 1 = 4πL MKK 2 ( D ) 23 ( D ) 21 [ αs 2 (1 1 ) + αq 2 d N + α c s 2 wc 2 (T3 d Q ds 2 w) 2 ], w C 1 = 4πL MKK 2 ( d ) 23 ( d ) 21 [ αs 2 (1 1 ) + αq 2 d N + α c s 2 ( Q d s 2 w) 2 ], w c2 w C 4 = 4πLαs MKK 2 ( D ) 23 ( d ) 21 L πβmkk 2 ( Ω d ) 23 ( Ω D ) 21, C 4 = 4πLαs MKK 2 ( d ) 23 ( L D ) 21 πβmkk 2 ( Ω D ) 23 ( Ω d ) 21, C 5 = 4πL MKK 2 ( D ) 23 ( d ) 21 [ αs 2αQ 2 d N + 2α c s 2 (T w c2 3 d Q ds 2 w )(Q ds 2 w )], w C 5 = 4πL MKK 2 ( d ) 23 ( D ) 21 [ αs 2αQ 2 d N + 2α c s 2 wc 2 (T3 d Q ds 2 w )(Q ds 2 w )], w F. Munir (IHEP) New Physics 9 / 14
10 b ss d decay in the bulk-higgs RS model ( D ) 23 ( d ) 21 (U d ) 2i(U d ) i3 ( Dd ) ij (W d ) 2j(W d ) j1, ( Dd ) ij = F 2 (c Qi ) 3 + 2c Qi 3 + c Qi + c dj F 2 (c dj ), 2(2 + c Qi + c dj ) 3 + 2c dj ( Ω D ) 23 ( Ω d ) 21 (U d ) 2i(W d ) j3 ( Ω Dd ) ijkl (W d ) 2k(U d ) l1, π(1 + β) ( Ω Dd ) ijkl = 4L The decay width in the bulk-higgs RS model F (c Qi )F (c dj ) (Y d ) ij (Y 2 + β + c Qi + c dj 1 d ) kl (4 + 2β + c Qi + c dj + c dk + c Ql ) 4 + c Qi + c dj + c dk + c Ql F (c dk )F (c Ql ) 2 + β + c dk + c Ql, Γ = m 5 b 3072(2π) 3 [64( C 1(µ b ) 2 + C 1 (µ b ) 2 ) + 12( C 4 (µ b ) 2 + C 4 (µ b ) 2 + C 5 (µ b ) 2 + C 5 (µ b ) 2 ) + 4Re(C 4 (µ b )C 5 (µ b) + C 4 (µ b)c 5 (µ b ) + C 4 (µ b ) C 5 (µ b) + C 4 (µ b) C 5 (µ b ))]. F. Munir (IHEP) New Physics 10 / 14
11 Phenomenological bounds on RS models The RS c model Constraint from tree-level analysis of the S and T parameters [Malm, Neubert, Novotny, Schmell, JHEP 01 (2014) 173] M g (1) > 4.8 TeV (95% CL). [Malm, Neubert, Schmell, JHEP 02 (2015) 008] Stringent bounds emerge from the signal rates for pp h ZZ, W W, at 95% CL M g (1) custodial RS brane-higgs > 22.7 TeV ( y 3 ), M RS g (1) custodial narrow bulk- > 13.2 TeV ( y Higgs 3 ) F. Munir (IHEP) New Physics 11 / 14
12 Branching ratio of b ssd in the RSc model MK, ǫk and MBs constraints KK gluons dominant Comparable ZH and Z contributions F. Munir (IHEP) New Physics 12 / 14
13 Branching ratio in the bulk-higgs RS model broad Higgs profile narrow Higgs profile β=1 F. Munir (IHEP) β = 10 New Physics 13 / 14
14 Summary In both models, the main contribution to the b ss d decay comes from tree level exchanges of KK gluons, while in the RS c model the contributions from the new heavy EW gauge bosons Z H and Z can compete with the KK-gluon contributions. We employed renormalization group runnings of the Wilson coefficients with NLO QCD factors in both models. The RS c model enhances the branching ratio, compared to the SM result, by two order of magnitude for some points in the parameter space with y = 1.5. In the bulk-higgs RS model with β = 10, it is possible to achieve an order of magnitude enhancement of the branching ratio for some of the parameter points. THANK YOU! F. Munir (IHEP) New Physics 14 / 14
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